scholarly journals Hidden zero-temperature bicritical point in the two-dimensional anisotropic Heisenberg model: Monte Carlo simulations and proper finite-size scaling

2006 ◽  
Vol 74 (6) ◽  
Author(s):  
Chenggang Zhou ◽  
D. P. Landau ◽  
T. C. Schulthess
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Heisenberg Model ◽  
Finite Size ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Anisotropic Heisenberg Model

scholarly journals Extrapolating Monte Carlo Simulations to Infinite Volume: Finite-Size Scaling atξ/L≫1

1995 ◽  
Vol 74 (15) ◽  
pp. 2969-2972 ◽  
Author(s):  
Sergio Caracciolo ◽  
Robert G. Edwards ◽  
Sabino José Ferreira ◽  
Andrea Pelissetto ◽  
Alan D. Sokal
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Finite Size ◽  
Infinite Volume ◽  
Finite Size Scaling ◽  
Size Scaling

HOW MONTE CARLO SIMULATIONS CAN CLARIFY COMPLEX PROBLEMS IN STATISTICAL PHYSICS

2001 ◽  
Vol 15 (09) ◽  
pp. 1193-1211 ◽  
Author(s):  
KURT BINDER
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Statistical Physics ◽  
Condensed Matter ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Complex Phase ◽  
Finite Systems ◽  
Scaling Methods

Statistical mechanics of condensed matter systems in physics (fluids and solids) derives macroscopic equilibrium properties of these systems as averages computed from a Hamiltonian that describes the atomistic interactions in the system. While analytic methods for most problems involve uncontrolled approximations, Monte Carlo simulations allow numerically exact treatments, apart from statistical errors and from the systematic problem that finite systems are treated rather than the thermodynamic limit. However, this problem can be overcome by finite size scaling methods, and thus Monte Carlo methods have become a very powerful tool to study even complex phase transitions. Examples given will include unmixing of polymer blends, two-dimensional melting, etc.

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